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📰 Solution: The dot product of two unit vectors is $\mathbf{u} \cdot \mathbf{v} = \cos\theta$. Given $\cos\theta = \frac{\sqrt{3}}{2}$, the angle $\theta$ satisfies $\theta = \arccos\left(\frac{\sqrt{3}}{2}\right)$. This corresponds to $\theta = 30^\circ$ or $\frac{\pi}{6}$ radians. However, since cosine is positive in both the first and fourth quadrants, but angles between vectors are typically taken in $[0, \pi]$, the solution is $\boxed{\dfrac{\pi}{6}}$. 📰 Question: A biochemistry technician measures the angle between two molecular bonds modeled as vectors $\mathbf{a} = \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 0 \\ 1 \\ 1 \end{pmatrix}$. Compute $\cos\theta$ where $\theta$ is the angle between them. 📰 Solution: The cosine of the angle between vectors $\mathbf{a}$ and $\mathbf{b}$ is given by $\cos\theta = \frac{\mathbf{a} \cdot \mathbf{b}}{\|\mathbf{a}\| \|\mathbf{b}\|}$. Compute the dot product: $\mathbf{a} \cdot \mathbf{b} = (1)(0) + (0)(1) + (1)(1) = 1$. The magnitudes are $\|\mathbf{a}\| = \sqrt{1^2 + 0^2 + 1^2} = \sqrt{2}$ and $\|\mathbf{b}\| = \sqrt{0^2 + 1^2 + 1^2} = \sqrt{2}$. Thus, $\cos\theta = \frac{1}{\sqrt{2} \cdot \sqrt{2}} = \frac{1}{2}$. The final answer is $\boxed{\dfrac{1}{2}}$. 📰 Pubg Extraction Shooter 1585006 📰 Height Map Roblox 781757 📰 Kill Bill Movie 2668421 📰 This Leather Reclining Sofa Will Turn Your Living Room Into A Luxury Oasis 4188190 📰 Double Cross Nation A Washington Insiders Gripping Tale Of Political Conspiracy 9595597 📰 Baint 9411707 📰 Mr Adams Headshots Locations 4887727 📰 Heart Eyes Reviews 3609824 📰 Gg Karate Roblox 4995677 📰 You Wont Believe How Cn Rail Transformed Freight Transport Forever 7648810 📰 Each Patient Profile Takes 025 Seconds To Load 6363742 📰 Application Builder No Coding 6308409 📰 5 Is This The Most Powerful Thor Costume Youve Ever Seen Watch Before It Breaks The Internet 4671757 📰 Truetype Unleashed The Revolutionary Font Transforming Design Forever 6402430 📰 New Port Richey Fl 5733601